Texture shift when character moves

I was working on the texture of a character using planar mapping (I deleted all UVs then reselect the faces to make a new map). The map is ok when the character does not move but once I move his joints, the map does not follow and acts like a projection map.
I notice the UV map in the UV texture editor moves with my character therefore my map shifts.

My teacher suggested to move the SkinCluster input up so it happens before the mapping. However I cannot move it before all my actions of the new maps.

I was also working with nCloth. My nCloth objects does the same thing. I have not created new UV map this time.

I tried using a reference object but it did not work.

What is happening and how can i fix it?

Thank you so much for helping!!